A Mathematical Analysis of Digestive Processes in a Model Stomach
It is of great medical interest to gain a better understanding of digestion in the human stomach, not least because of the relevance to nutrient and drug delivery. The Institute of Food Research has developed the Dynamic Gastric Model, a physical, in vitro model stomach capable of re-creating the physiological conditions experienced in vivo. The aim of this thesis is to examine mathematically digestion in the main body (top section) of the Dynamic Gastric Model, where gentle wall movements and gastric secretions result in the outside layer of the digesta “sloughing off”, before passing into the bottom section for further processing. By considering a simplified, local description of the flow close to the wall, we may gain an insight into the mechanisms behind this behaviour. This description focuses on the mixing of two layers of creeping fluid through temporal instability of the perturbed fluid interface. Some attention is also paid to a more general study of the surrounding flow field. Linear, two-fluid flow next to a prescribed, sinusoidally moving wall is found to be stable in all cases. Studies of thin film flow next to such a wall suggest that the same may be true of the nonlinear case, although in the case of an inclined wall wave steepening is found to occur for early times. A linear instability is found for small wavenumber disturbances when the wall is modelled as an elastic beam or when we include a scalar material field that acts to alter the surface tension at the interface. An examination of Navier–Stokes flow of a single fluid through a diverging channel (representing a small strip through the centre of the main body) reveals that the flow loses symmetry at a lower Reynolds number than flow through a channel of uniform width. Our results are interpreted in terms of the Dynamic Gastric Model.
Networked Digital Library of Theses and Dissertations